If R is the midpoint of QS, RS=2X-4, ST=4X-1, and RT=8X-43, find QS
1 answer:
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Draw a diagram to illustrate the problem as shown below.
When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.
Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
Answer:
The smaller gear makes 1.75 rotations
When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.
Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
Answer:
The smaller gear makes 1.75 rotations
For the units positions of all numbers we have:
From this we can conclude that total sum of these three numbers is 14. Number 1 we carry to next step. So we have:
For the tens positions of all numbers we have:
The extra number 1 on left side comes from the carry from last step. Similar to ones position we know that total sum is 11.
Now we insert x and z to find out y:
Now we need to find out the product of these three numbers:
From this we can conclude that total sum of these three numbers is 14. Number 1 we carry to next step. So we have:
For the tens positions of all numbers we have:
The extra number 1 on left side comes from the carry from last step. Similar to ones position we know that total sum is 11.
Now we insert x and z to find out y:
Now we need to find out the product of these three numbers: